Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pelagic 12 3.765594
beta1_pelagic 15 2.935397
beta1_yellow 12 2.600049
mu_beta0_pH 5 2.214647
beta0_yellow 10 2.146612
beta0_pH 34 2.145554
beta1_black 9 1.875058
beta1_pH 25 1.780964
sd_comp 1 1.725599
beta3_pelagic 15 1.703679
beta3_pH 28 1.612519
beta2_pH 21 1.562844
beta3_black 11 1.536711
tau_beta0_pelagic 2 1.439983
parameter n badRhat_avg
beta3_yellow 12 1.404400
mu_beta0_pelagic 2 1.397365
beta2_yellow 9 1.377338
beta2_pelagic 15 1.360253
beta2_black 10 1.348542
mu_beta0_yellow 2 1.338795
beta0_black 8 1.337951
tau_beta0_black 1 1.284012
tau_beta0_yellow 3 1.271521
tau_beta0_pH 5 1.190044
beta4_pelagic 2 1.132910
beta_H 1 1.129128
beta4_black 1 1.112162
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
beta0_black 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0
beta0_pelagic 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0
beta0_pH 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta0_yellow 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1
beta1_black 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0
beta1_pelagic 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1
beta1_pH 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1
beta1_yellow 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1
beta2_black 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0
beta2_pelagic 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta2_pH 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 0
beta2_yellow 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1
beta3_black 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1
beta3_pelagic 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
beta3_pH 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1
beta3_yellow 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1
beta4_black 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
beta4_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0
mu_beta0_pelagic 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0
mu_beta0_pH 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0
mu_beta0_yellow 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.168 0.069 -0.293 -0.169 -0.027
mu_bc_H[2] -0.110 0.037 -0.177 -0.113 -0.032
mu_bc_H[3] -0.451 0.066 -0.578 -0.451 -0.317
mu_bc_H[4] -1.087 0.197 -1.492 -1.088 -0.715
mu_bc_H[5] 0.613 0.740 -0.275 0.506 2.299
mu_bc_H[6] -2.307 0.314 -2.916 -2.311 -1.671
mu_bc_H[7] -0.449 0.111 -0.676 -0.447 -0.238
mu_bc_H[8] 0.103 0.355 -0.516 0.078 0.864
mu_bc_H[9] -0.317 0.128 -0.580 -0.318 -0.058
mu_bc_H[10] -0.127 0.068 -0.254 -0.129 0.008
mu_bc_H[11] -0.127 0.035 -0.196 -0.127 -0.057
mu_bc_H[12] -0.274 0.106 -0.506 -0.266 -0.078
mu_bc_H[13] -0.153 0.074 -0.297 -0.155 -0.007
mu_bc_H[14] -0.311 0.094 -0.500 -0.310 -0.130
mu_bc_H[15] -0.347 0.050 -0.438 -0.348 -0.248
mu_bc_H[16] -0.250 0.390 -0.900 -0.285 0.562
mu_bc_R[1] 0.609 1.763 -3.570 1.212 2.716
mu_bc_R[2] -0.357 2.078 -5.347 0.479 2.062
mu_bc_R[3] 0.226 1.942 -5.103 0.951 2.133
mu_bc_R[4] -1.508 2.138 -6.619 -0.760 1.022
mu_bc_R[5] 1.320 1.542 -1.875 1.312 4.306
mu_bc_R[6] -0.798 1.363 -4.023 -0.555 1.191
mu_bc_R[7] 1.581 1.338 -2.722 2.000 2.820
mu_bc_R[8] 1.141 0.901 -1.193 1.341 2.360
mu_bc_R[9] 1.538 1.368 -1.933 1.811 3.277
mu_bc_R[10] 0.657 1.939 -3.765 1.045 3.579
mu_bc_R[11] -2.246 0.899 -4.003 -2.232 -0.451
mu_bc_R[12] -3.265 1.054 -5.429 -3.184 -1.286
mu_bc_R[13] -2.515 0.979 -4.560 -2.431 -0.663
mu_bc_R[14] -2.480 0.965 -4.463 -2.440 -0.620
mu_bc_R[15] -2.084 0.911 -4.087 -2.036 -0.512
mu_bc_R[16] -1.703 1.212 -4.182 -1.620 0.534
tau_pH[1] 8101.384 40335.166 94.804 869.243 52997.432
tau_pH[2] 2.387 0.366 1.657 2.383 3.101
tau_pH[3] 2.681 0.414 1.953 2.662 3.539
tau_pH[4] 10.105 4.463 3.848 9.554 20.918
tau_pH[5] 2.606 1.898 0.331 2.370 6.972
beta0_pH[1,1] 0.802 1.935 -3.520 1.435 3.424
beta0_pH[2,1] 0.507 2.144 -4.575 1.303 3.188
beta0_pH[3,1] 1.055 2.110 -4.476 1.713 3.571
beta0_pH[4,1] 0.066 2.280 -5.259 0.844 2.969
beta0_pH[5,1] 1.440 1.688 -2.163 1.438 4.979
beta0_pH[6,1] 2.845 1.871 0.009 2.644 6.842
beta0_pH[7,1] 2.851 2.625 -2.702 2.686 8.685
beta0_pH[8,1] 0.691 1.091 -1.858 0.846 2.426
beta0_pH[9,1] 1.711 1.640 -2.227 1.864 4.334
beta0_pH[10,1] 0.791 1.990 -3.705 1.170 3.934
beta0_pH[11,1] -3.242 0.937 -5.099 -3.187 -1.380
beta0_pH[12,1] -3.220 1.046 -5.383 -3.119 -1.250
beta0_pH[13,1] -3.047 1.043 -5.115 -2.990 -0.963
beta0_pH[14,1] -3.154 0.980 -5.187 -3.081 -1.271
beta0_pH[15,1] -2.838 0.976 -4.908 -2.819 -1.060
beta0_pH[16,1] -3.054 1.168 -5.555 -2.972 -0.813
beta0_pH[1,2] 2.424 0.242 1.982 2.415 2.933
beta0_pH[2,2] 2.524 0.365 1.811 2.528 3.156
beta0_pH[3,2] 2.410 0.286 1.839 2.404 3.019
beta0_pH[4,2] 2.353 0.321 1.673 2.359 2.946
beta0_pH[5,2] 4.127 1.188 2.388 3.966 6.929
beta0_pH[6,2] 3.037 0.256 2.443 3.063 3.462
beta0_pH[7,2] 1.955 0.200 1.504 1.973 2.299
beta0_pH[8,2] 2.834 0.195 2.434 2.844 3.178
beta0_pH[9,2] 3.263 0.415 2.125 3.346 3.797
beta0_pH[10,2] 3.656 0.370 2.395 3.721 4.114
beta0_pH[11,2] -5.247 0.501 -6.424 -5.116 -4.390
beta0_pH[12,2] -5.096 0.455 -6.146 -5.053 -4.302
beta0_pH[13,2] -4.819 0.360 -5.540 -4.819 -4.133
beta0_pH[14,2] -5.546 0.419 -6.358 -5.518 -4.786
beta0_pH[15,2] -4.487 0.407 -5.267 -4.502 -3.667
beta0_pH[16,2] -4.995 0.408 -5.835 -4.990 -4.194
beta0_pH[1,3] 1.254 0.329 0.398 1.295 1.753
beta0_pH[2,3] 1.781 0.605 -0.040 1.967 2.459
beta0_pH[3,3] 1.772 0.627 0.416 1.839 2.689
beta0_pH[4,3] 2.196 0.688 0.870 2.220 3.151
beta0_pH[5,3] 0.294 1.470 -2.524 0.265 3.500
beta0_pH[6,3] -1.220 1.760 -5.564 -0.669 0.806
beta0_pH[7,3] -0.457 0.995 -2.322 -0.472 0.965
beta0_pH[8,3] 0.334 0.179 -0.035 0.337 0.670
beta0_pH[9,3] 0.007 0.388 -0.771 0.032 0.664
beta0_pH[10,3] 0.660 0.374 -0.250 0.709 1.276
beta0_pH[11,4] 0.030 1.652 -2.493 -0.017 2.817
beta0_pH[12,4] -0.828 1.958 -2.753 -1.963 2.873
beta0_pH[13,4] -0.064 1.565 -2.488 0.268 2.163
beta0_pH[14,4] 0.046 1.940 -2.784 0.284 3.031
beta0_pH[15,4] 0.317 1.720 -2.477 1.005 2.632
beta0_pH[16,4] -0.107 1.914 -4.088 0.177 2.381
beta0_pH[11,5] -0.429 0.636 -1.389 -0.537 0.907
beta0_pH[12,5] -1.223 1.276 -3.036 -1.123 1.007
beta0_pH[13,5] -0.176 0.507 -0.963 -0.246 0.912
beta0_pH[14,5] -0.626 0.682 -1.491 -0.865 0.819
beta0_pH[15,5] -0.712 0.634 -1.498 -0.974 0.518
beta0_pH[16,5] -0.454 0.531 -1.097 -0.656 0.832
beta1_pH[1,1] 1.456 0.484 0.826 1.357 2.672
beta1_pH[2,1] 0.785 0.227 0.463 0.750 1.370
beta1_pH[3,1] 0.944 0.287 0.497 0.910 1.592
beta1_pH[4,1] 0.959 0.442 0.270 0.905 1.956
beta1_pH[5,1] 1.431 1.068 0.226 1.219 3.689
beta1_pH[6,1] 1.987 2.324 0.332 1.296 8.268
beta1_pH[7,1] 1.544 1.678 0.203 1.138 5.879
beta1_pH[8,1] 1.654 0.467 0.851 1.627 2.645
beta1_pH[9,1] 1.211 0.903 0.221 1.092 3.006
beta1_pH[10,1] 0.940 0.176 0.608 0.933 1.298
beta1_pH[11,1] 2.248 0.212 1.847 2.242 2.665
beta1_pH[12,1] 1.454 0.376 0.867 1.414 2.293
beta1_pH[13,1] 1.783 0.324 1.183 1.773 2.443
beta1_pH[14,1] 1.507 0.304 1.012 1.493 2.024
beta1_pH[15,1] 1.534 0.424 0.847 1.482 2.529
beta1_pH[16,1] 3.354 0.557 2.520 3.265 4.713
beta1_pH[1,2] 1.143 0.624 0.036 1.124 2.207
beta1_pH[2,2] 0.843 1.624 0.014 0.764 1.925
beta1_pH[3,2] 1.178 0.377 0.180 1.195 1.862
beta1_pH[4,2] 0.921 1.506 0.019 0.815 2.089
beta1_pH[5,2] 1.174 8.142 0.000 0.001 5.637
beta1_pH[6,2] 0.269 0.624 0.000 0.002 2.015
beta1_pH[7,2] 0.132 0.364 0.000 0.001 1.300
beta1_pH[8,2] 0.148 0.371 0.000 0.003 1.253
beta1_pH[9,2] 0.202 0.480 0.000 0.001 1.732
beta1_pH[10,2] 0.153 0.423 0.000 0.001 1.537
beta1_pH[11,2] 7.322 0.762 6.371 7.057 9.294
beta1_pH[12,2] 7.170 0.591 6.151 7.117 8.473
beta1_pH[13,2] 7.380 0.406 6.590 7.373 8.197
beta1_pH[14,2] 7.493 0.465 6.636 7.464 8.392
beta1_pH[15,2] 7.076 0.458 6.166 7.085 8.004
beta1_pH[16,2] 7.748 0.451 6.867 7.740 8.633
beta1_pH[1,3] 2.056 0.492 1.259 1.995 3.313
beta1_pH[2,3] 1.239 1.249 0.001 0.959 4.024
beta1_pH[3,3] 1.049 0.736 0.001 0.971 2.756
beta1_pH[4,3] 1.316 1.899 0.001 1.145 4.070
beta1_pH[5,3] 2.595 3.741 0.216 2.062 7.838
beta1_pH[6,3] 2.795 5.488 0.152 1.996 9.152
beta1_pH[7,3] 1.840 1.302 0.152 1.784 3.989
beta1_pH[8,3] 2.683 0.339 2.034 2.682 3.375
beta1_pH[9,3] 2.077 0.436 1.319 2.058 2.955
beta1_pH[10,3] 2.715 0.450 1.963 2.667 3.759
beta1_pH[11,4] 4.176 2.968 0.078 4.300 11.354
beta1_pH[12,4] 3.790 1.943 0.079 4.876 5.814
beta1_pH[13,4] 3.121 1.884 0.094 3.096 6.623
beta1_pH[14,4] 3.845 3.380 0.060 3.489 14.643
beta1_pH[15,4] 2.608 1.781 0.075 1.886 5.567
beta1_pH[16,4] 3.295 2.015 0.064 3.615 7.345
beta1_pH[11,5] 2.757 2.519 0.008 2.049 9.114
beta1_pH[12,5] 10.801 16.003 0.236 5.952 67.747
beta1_pH[13,5] 7.531 10.396 0.435 4.794 33.162
beta1_pH[14,5] 3.772 3.349 0.006 3.010 11.997
beta1_pH[15,5] 5.073 3.606 0.183 4.137 12.596
beta1_pH[16,5] 4.437 7.294 0.006 2.827 17.050
beta2_pH[1,1] 1.872 2.749 0.150 0.691 10.405
beta2_pH[2,1] 2.627 3.049 0.179 1.521 11.037
beta2_pH[3,1] 3.498 3.352 0.404 2.417 12.581
beta2_pH[4,1] 2.872 3.632 -1.417 1.918 12.904
beta2_pH[5,1] 3.926 4.224 -0.211 2.883 15.743
beta2_pH[6,1] 3.757 4.077 -2.043 2.860 14.256
beta2_pH[7,1] 2.413 4.984 -8.936 2.194 12.943
beta2_pH[8,1] 3.568 3.627 0.277 2.543 13.656
beta2_pH[9,1] 3.266 4.598 -6.316 2.648 14.073
beta2_pH[10,1] 4.566 4.472 0.445 2.885 16.730
beta2_pH[11,1] 0.733 0.298 0.437 0.685 1.266
beta2_pH[12,1] 0.716 0.720 0.137 0.541 2.450
beta2_pH[13,1] 0.526 0.340 0.209 0.456 1.325
beta2_pH[14,1] 1.079 1.012 0.223 0.839 3.492
beta2_pH[15,1] 0.471 0.521 0.096 0.341 1.698
beta2_pH[16,1] 0.309 0.172 0.159 0.296 0.516
beta2_pH[1,2] 3.484 4.535 -5.539 2.654 13.999
beta2_pH[2,2] -3.836 5.704 -17.077 -3.073 7.869
beta2_pH[3,2] -4.720 4.368 -16.432 -3.503 -0.476
beta2_pH[4,2] -4.652 4.937 -16.437 -3.623 3.473
beta2_pH[5,2] -0.205 6.398 -13.292 -0.332 13.291
beta2_pH[6,2] -0.817 6.584 -14.539 -0.964 12.746
beta2_pH[7,2] -0.395 6.601 -14.276 -0.464 13.369
beta2_pH[8,2] -0.435 6.517 -14.189 -0.550 13.123
beta2_pH[9,2] -0.765 6.333 -13.698 -1.030 12.536
beta2_pH[10,2] -0.247 6.711 -13.782 -0.412 13.882
beta2_pH[11,2] -3.860 2.103 -7.079 -4.216 -0.333
beta2_pH[12,2] -1.524 1.221 -4.675 -1.155 -0.477
beta2_pH[13,2] -2.639 0.954 -5.362 -2.512 -1.291
beta2_pH[14,2] -3.296 1.130 -5.814 -3.190 -1.444
beta2_pH[15,2] -5.602 2.670 -12.300 -4.926 -2.285
beta2_pH[16,2] -6.185 2.842 -13.623 -5.467 -2.827
beta2_pH[1,3] 3.777 3.582 0.302 2.727 13.837
beta2_pH[2,3] 2.360 3.979 -4.391 1.089 12.789
beta2_pH[3,3] 1.876 5.208 -9.167 1.704 13.505
beta2_pH[4,3] 2.482 3.956 -4.283 1.865 12.090
beta2_pH[5,3] 3.185 5.975 -10.231 3.551 15.280
beta2_pH[6,3] 3.778 5.718 -9.293 3.982 15.704
beta2_pH[7,3] 3.846 5.553 -8.567 3.912 15.511
beta2_pH[8,3] 7.156 3.815 2.068 6.416 15.917
beta2_pH[9,3] 5.890 3.824 1.073 5.013 15.648
beta2_pH[10,3] 3.972 3.331 0.505 3.122 13.044
beta2_pH[11,4] -0.166 1.782 -3.149 -0.200 3.862
beta2_pH[12,4] -0.571 1.146 -2.078 -0.845 2.744
beta2_pH[13,4] -0.325 2.494 -6.428 0.171 4.250
beta2_pH[14,4] -0.268 2.646 -5.255 -0.682 5.279
beta2_pH[15,4] -0.245 2.062 -3.851 0.361 2.451
beta2_pH[16,4] -0.583 2.637 -5.717 -0.836 5.243
beta2_pH[11,5] -0.525 2.571 -6.125 -0.356 3.375
beta2_pH[12,5] -2.257 1.908 -6.781 -1.970 1.829
beta2_pH[13,5] -2.335 1.330 -5.448 -2.448 -0.136
beta2_pH[14,5] -2.149 2.487 -8.607 -1.744 0.042
beta2_pH[15,5] -2.022 2.156 -6.591 -2.010 2.141
beta2_pH[16,5] -2.070 3.005 -8.796 -1.975 4.050
beta3_pH[1,1] 34.687 2.349 30.946 34.528 40.325
beta3_pH[2,1] 36.327 1.640 33.917 36.075 40.841
beta3_pH[3,1] 33.423 2.104 30.369 33.597 35.693
beta3_pH[4,1] 38.934 9.645 25.980 37.949 52.887
beta3_pH[5,1] 43.745 59.186 17.971 39.938 64.944
beta3_pH[6,1] 31.766 10.301 14.073 33.026 52.351
beta3_pH[7,1] 34.862 13.926 11.400 33.964 66.986
beta3_pH[8,1] 31.922 2.374 28.164 31.792 35.829
beta3_pH[9,1] 34.657 22.847 11.952 29.722 78.906
beta3_pH[10,1] 34.596 1.977 29.972 34.942 36.687
beta3_pH[11,1] 30.195 0.517 29.100 30.214 31.180
beta3_pH[12,1] 31.483 2.466 27.476 31.169 36.720
beta3_pH[13,1] 34.681 1.732 31.998 34.486 38.200
beta3_pH[14,1] 30.880 1.384 28.336 30.908 33.176
beta3_pH[15,1] 33.593 2.880 28.723 33.296 40.242
beta3_pH[16,1] 33.607 1.166 30.903 33.702 35.647
beta3_pH[1,2] 40.320 12.453 9.625 40.732 50.817
beta3_pH[2,2] 42.847 18.910 4.496 42.887 82.871
beta3_pH[3,2] 41.811 7.567 38.056 41.962 45.479
beta3_pH[4,2] 39.894 16.430 5.227 41.479 63.102
beta3_pH[5,2] 72.985 144.748 0.323 32.778 421.529
beta3_pH[6,2] 58.895 170.276 0.200 31.905 328.256
beta3_pH[7,2] 48.341 66.932 0.268 33.717 167.694
beta3_pH[8,2] 88.691 84.409 0.729 49.754 230.645
beta3_pH[9,2] 88.635 240.017 0.352 35.287 745.089
beta3_pH[10,2] 80.404 110.604 0.417 40.662 375.480
beta3_pH[11,2] 43.319 0.259 42.612 43.342 43.697
beta3_pH[12,2] 43.029 0.321 42.314 43.056 43.610
beta3_pH[13,2] 43.807 0.172 43.448 43.818 44.141
beta3_pH[14,2] 43.266 0.146 42.988 43.260 43.559
beta3_pH[15,2] 43.430 0.174 43.140 43.417 43.791
beta3_pH[16,2] 43.468 0.159 43.176 43.466 43.768
beta3_pH[1,3] 39.825 1.067 36.697 40.001 41.336
beta3_pH[2,3] 46.700 56.188 4.097 34.377 170.844
beta3_pH[3,3] 29.811 22.317 0.202 31.639 89.035
beta3_pH[4,3] 87.272 209.001 0.858 27.273 936.749
beta3_pH[5,3] 39.333 25.871 12.699 34.228 93.658
beta3_pH[6,3] 41.381 20.332 15.104 38.093 85.948
beta3_pH[7,3] 33.993 18.914 15.053 28.883 65.255
beta3_pH[8,3] 41.485 0.233 41.063 41.488 41.916
beta3_pH[9,3] 33.760 0.533 32.840 33.784 34.778
beta3_pH[10,3] 35.824 0.735 33.808 35.996 36.840
beta3_pH[11,4] 39.853 10.768 17.132 42.410 60.017
beta3_pH[12,4] 40.357 7.314 23.117 42.164 51.593
beta3_pH[13,4] 36.636 6.495 24.878 35.465 44.612
beta3_pH[14,4] 41.925 9.261 25.290 42.222 55.337
beta3_pH[15,4] 40.263 9.084 29.540 39.869 57.001
beta3_pH[16,4] 41.907 7.172 23.992 44.288 50.358
beta3_pH[11,5] 74.528 97.370 7.418 39.900 403.561
beta3_pH[12,5] 38.436 7.307 16.603 38.583 55.695
beta3_pH[13,5] 66.120 73.899 28.123 40.831 350.027
beta3_pH[14,5] 28.249 17.827 0.178 38.438 51.892
beta3_pH[15,5] 36.041 11.327 0.570 40.109 41.971
beta3_pH[16,5] 31.145 26.371 2.806 32.208 60.344
beta0_pelagic[1] 1.289 0.771 -0.020 1.285 2.374
beta0_pelagic[2] 0.893 0.508 -0.028 0.859 1.607
beta0_pelagic[3] 0.391 0.289 -0.185 0.383 0.875
beta0_pelagic[4] -0.998 1.880 -3.877 0.229 0.597
beta0_pelagic[5] -1.069 2.891 -7.094 0.973 1.490
beta0_pelagic[6] 1.105 0.563 -0.278 1.348 1.700
beta0_pelagic[7] 1.618 0.136 1.360 1.619 1.889
beta0_pelagic[8] 1.707 0.165 1.326 1.716 1.988
beta0_pelagic[9] 2.632 0.294 1.771 2.694 3.008
beta0_pelagic[10] 2.528 0.155 2.177 2.538 2.785
beta0_pelagic[11] 0.187 0.395 -0.639 0.286 0.820
beta0_pelagic[12] 1.685 0.159 1.362 1.683 1.994
beta0_pelagic[13] 0.326 0.187 -0.033 0.350 0.663
beta0_pelagic[14] -0.089 0.214 -0.573 -0.068 0.305
beta0_pelagic[15] -0.246 0.154 -0.509 -0.266 0.118
beta0_pelagic[16] 0.359 0.155 0.037 0.363 0.636
beta1_pelagic[1] 0.925 0.774 0.000 0.913 2.277
beta1_pelagic[2] 0.645 0.550 0.000 0.677 1.606
beta1_pelagic[3] 0.573 0.465 0.000 0.644 1.440
beta1_pelagic[4] 2.604 2.356 0.594 1.031 6.685
beta1_pelagic[5] 2.337 2.989 0.000 0.011 8.617
beta1_pelagic[6] 0.412 0.651 0.000 0.001 1.997
beta1_pelagic[7] 0.454 4.417 0.000 0.000 1.254
beta1_pelagic[8] 0.091 0.912 0.000 0.000 0.576
beta1_pelagic[9] 0.215 0.567 0.000 0.000 1.513
beta1_pelagic[10] 0.073 0.272 0.000 0.000 0.709
beta1_pelagic[11] 3.106 0.811 2.028 2.987 4.693
beta1_pelagic[12] 2.672 0.328 2.049 2.704 3.297
beta1_pelagic[13] 3.460 1.463 1.725 2.939 6.899
beta1_pelagic[14] 4.307 0.998 2.974 4.063 6.883
beta1_pelagic[15] 2.887 0.256 2.434 2.869 3.408
beta1_pelagic[16] 3.309 0.416 2.663 3.244 4.318
beta2_pelagic[1] 1.276 4.247 -7.093 0.066 11.415
beta2_pelagic[2] 1.489 4.020 -7.380 0.830 11.281
beta2_pelagic[3] 1.723 4.240 -7.195 1.004 11.679
beta2_pelagic[4] 1.930 2.944 0.032 0.688 10.615
beta2_pelagic[5] -4.150 7.359 -18.858 -4.169 9.722
beta2_pelagic[6] 1.555 6.582 -12.241 1.629 15.498
beta2_pelagic[7] 1.124 5.449 -11.313 1.891 9.678
beta2_pelagic[8] -0.327 6.751 -14.826 -0.201 13.384
beta2_pelagic[9] -0.299 5.919 -11.784 -2.064 13.478
beta2_pelagic[10] 0.556 5.968 -12.492 1.270 12.793
beta2_pelagic[11] 1.602 2.627 0.157 0.445 8.831
beta2_pelagic[12] 5.699 3.660 1.490 4.750 15.352
beta2_pelagic[13] 0.786 1.101 0.182 0.387 4.262
beta2_pelagic[14] 0.336 0.169 0.166 0.302 0.801
beta2_pelagic[15] 5.555 3.777 1.114 4.462 14.821
beta2_pelagic[16] 4.557 4.333 0.376 3.538 15.538
beta3_pelagic[1] 57.034 106.287 0.267 26.021 372.952
beta3_pelagic[2] 86.278 383.958 0.371 18.493 688.531
beta3_pelagic[3] 40.592 83.176 0.321 29.065 190.548
beta3_pelagic[4] 19.540 10.338 0.100 25.069 32.280
beta3_pelagic[5] 136.655 486.452 1.545 46.455 1557.909
beta3_pelagic[6] 95.797 243.835 1.370 30.005 886.479
beta3_pelagic[7] 54.454 39.697 1.325 44.512 144.356
beta3_pelagic[8] 56.100 116.988 0.555 33.142 403.466
beta3_pelagic[9] 55.435 29.259 8.826 57.701 122.568
beta3_pelagic[10] 41.209 45.920 0.867 27.898 194.132
beta3_pelagic[11] 42.101 1.517 38.101 42.556 43.974
beta3_pelagic[12] 43.448 0.238 43.029 43.441 43.904
beta3_pelagic[13] 43.893 2.356 40.626 43.076 48.960
beta3_pelagic[14] 42.602 1.512 40.184 42.339 45.927
beta3_pelagic[15] 43.193 0.286 42.415 43.215 43.667
beta3_pelagic[16] 43.096 0.405 42.094 43.187 43.689
mu_beta0_pelagic[1] 0.392 0.918 -1.829 0.421 2.270
mu_beta0_pelagic[2] 1.356 0.980 -1.246 1.635 2.675
mu_beta0_pelagic[3] 0.368 0.398 -0.436 0.385 1.083
tau_beta0_pelagic[1] 14.059 33.662 0.029 2.838 101.608
tau_beta0_pelagic[2] 1.632 2.007 0.037 0.979 6.757
tau_beta0_pelagic[3] 2.060 1.425 0.346 1.722 5.509
beta0_yellow[1] -0.522 0.190 -0.982 -0.506 -0.197
beta0_yellow[2] 0.467 0.178 0.003 0.478 0.780
beta0_yellow[3] -0.316 0.168 -0.681 -0.310 0.005
beta0_yellow[4] 0.794 0.278 -0.019 0.833 1.214
beta0_yellow[5] -0.825 0.582 -1.895 -0.846 0.249
beta0_yellow[6] 0.588 0.438 -0.057 0.461 1.363
beta0_yellow[7] 0.884 0.430 -0.428 0.995 1.344
beta0_yellow[8] 0.968 0.183 0.541 0.984 1.283
beta0_yellow[9] 0.223 0.426 -0.474 0.132 0.940
beta0_yellow[10] 0.366 0.228 -0.013 0.339 0.811
beta0_yellow[11] -1.817 1.277 -3.838 -1.476 0.109
beta0_yellow[12] -3.539 0.491 -4.474 -3.537 -2.657
beta0_yellow[13] -3.914 0.564 -4.985 -3.899 -2.834
beta0_yellow[14] -1.073 0.986 -3.188 -0.650 0.045
beta0_yellow[15] -2.160 0.732 -3.477 -2.329 -0.850
beta0_yellow[16] -1.863 0.728 -2.969 -2.008 -0.278
beta1_yellow[1] 0.565 0.568 0.000 0.467 1.919
beta1_yellow[2] 1.077 0.379 0.587 1.013 2.090
beta1_yellow[3] 0.667 0.225 0.145 0.675 1.090
beta1_yellow[4] 1.293 0.780 0.563 1.110 4.261
beta1_yellow[5] 1.742 1.478 0.000 1.917 4.182
beta1_yellow[6] 1.430 1.072 0.000 1.906 2.756
beta1_yellow[7] 1.302 1.641 0.000 0.478 4.943
beta1_yellow[8] 0.980 1.163 0.000 0.476 3.783
beta1_yellow[9] 1.018 0.906 0.000 1.232 2.827
beta1_yellow[10] 1.713 1.281 0.000 2.203 3.540
beta1_yellow[11] 1.928 1.197 0.000 1.595 3.846
beta1_yellow[12] 2.322 0.519 1.407 2.323 3.318
beta1_yellow[13] 3.096 0.587 1.966 3.076 4.231
beta1_yellow[14] 1.510 1.031 0.000 1.476 3.413
beta1_yellow[15] 1.554 0.771 0.002 1.744 2.889
beta1_yellow[16] 2.377 6.495 0.000 1.868 2.867
beta2_yellow[1] -2.465 3.484 -10.922 -1.779 3.475
beta2_yellow[2] -2.685 2.791 -10.365 -1.793 -0.132
beta2_yellow[3] -2.615 2.746 -10.756 -1.760 -0.198
beta2_yellow[4] -2.157 2.531 -9.314 -1.585 -0.088
beta2_yellow[5] -4.681 6.455 -18.516 -4.301 9.152
beta2_yellow[6] 3.676 5.991 -9.847 3.629 15.818
beta2_yellow[7] -2.357 6.233 -16.940 -1.536 9.826
beta2_yellow[8] -3.179 6.403 -16.889 -2.804 10.179
beta2_yellow[9] 3.562 6.393 -10.656 3.556 16.649
beta2_yellow[10] -4.192 5.653 -15.566 -3.876 8.505
beta2_yellow[11] -2.477 4.311 -12.294 -2.426 2.998
beta2_yellow[12] -4.824 3.396 -14.198 -3.917 -1.032
beta2_yellow[13] -4.711 3.034 -12.798 -3.898 -1.347
beta2_yellow[14] -3.976 4.346 -14.080 -3.430 4.023
beta2_yellow[15] -4.326 3.889 -13.888 -3.524 -0.159
beta2_yellow[16] -5.212 3.737 -15.020 -4.280 -0.842
beta3_yellow[1] 27.872 11.996 6.551 27.616 54.601
beta3_yellow[2] 29.590 2.163 25.405 29.276 34.512
beta3_yellow[3] 33.501 6.221 27.496 33.061 41.516
beta3_yellow[4] 30.636 3.291 23.854 31.608 36.278
beta3_yellow[5] 41.492 52.039 1.263 33.395 180.863
beta3_yellow[6] 42.552 38.699 1.232 39.476 145.710
beta3_yellow[7] 48.235 61.670 1.509 27.735 225.973
beta3_yellow[8] 44.315 73.823 1.641 28.667 270.703
beta3_yellow[9] 54.738 79.031 2.349 37.578 343.940
beta3_yellow[10] 41.773 70.625 1.940 29.420 227.939
beta3_yellow[11] 37.745 13.529 12.795 44.135 50.763
beta3_yellow[12] 43.416 0.505 42.515 43.376 44.519
beta3_yellow[13] 44.935 0.358 44.087 44.991 45.563
beta3_yellow[14] 43.770 13.025 23.310 44.006 82.673
beta3_yellow[15] 44.470 27.171 23.620 44.723 51.559
beta3_yellow[16] 44.385 6.743 34.960 44.436 48.961
mu_beta0_yellow[1] 0.083 0.436 -0.796 0.083 0.942
mu_beta0_yellow[2] 0.350 0.442 -0.553 0.369 1.146
mu_beta0_yellow[3] -2.010 0.819 -3.315 -2.069 -0.130
tau_beta0_yellow[1] 2.972 3.935 0.210 1.951 11.697
tau_beta0_yellow[2] 2.866 4.261 0.275 1.831 11.129
tau_beta0_yellow[3] 1.001 1.568 0.068 0.526 5.449
beta0_black[1] 0.089 0.198 -0.318 0.099 0.436
beta0_black[2] 1.755 0.442 0.146 1.869 2.139
beta0_black[3] 1.242 0.292 0.220 1.300 1.572
beta0_black[4] 2.150 0.393 1.094 2.218 2.633
beta0_black[5] 1.627 1.667 -1.233 1.670 4.253
beta0_black[6] 1.587 1.587 -1.423 1.653 4.213
beta0_black[7] 1.672 1.482 -1.027 1.692 4.244
beta0_black[8] 1.303 0.231 0.853 1.301 1.750
beta0_black[9] 2.366 0.283 1.791 2.368 2.882
beta0_black[10] 1.475 0.133 1.220 1.476 1.743
beta0_black[11] 3.303 0.416 2.052 3.408 3.754
beta0_black[12] 4.466 0.208 4.042 4.472 4.848
beta0_black[13] -0.072 0.239 -0.533 -0.081 0.392
beta0_black[14] 2.010 0.527 0.491 2.125 2.741
beta0_black[15] 1.125 0.286 0.400 1.179 1.552
beta0_black[16] 3.951 0.591 2.146 4.146 4.538
beta2_black[1] 2.115 5.625 -9.862 2.139 14.517
beta2_black[2] -0.057 4.172 -8.604 0.312 9.634
beta2_black[3] -1.721 6.134 -11.427 -1.256 11.005
beta2_black[4] -1.927 5.744 -14.578 -1.457 10.204
beta2_black[5] -0.141 6.279 -13.499 -0.081 12.816
beta2_black[6] -0.094 6.380 -13.576 -0.177 14.031
beta2_black[7] -0.155 6.295 -12.843 -0.243 12.976
beta2_black[8] -0.418 6.184 -13.689 -0.304 12.604
beta2_black[9] -0.091 6.105 -12.344 -0.199 12.925
beta2_black[10] 0.004 5.251 -9.675 -0.389 14.356
beta2_black[11] -0.359 4.005 -9.545 -0.451 6.529
beta2_black[12] -3.819 3.600 -11.716 -2.622 -0.278
beta2_black[13] -3.336 3.880 -15.952 -1.833 -0.520
beta2_black[14] -1.382 2.331 -9.809 -0.533 -0.094
beta2_black[15] -2.458 4.782 -14.206 -1.319 5.977
beta2_black[16] 0.643 3.614 -6.918 0.705 8.932
beta3_black[1] 66.041 156.864 0.339 41.377 401.404
beta3_black[2] 145.236 538.714 0.233 31.751 2560.631
beta3_black[3] 57.083 120.094 0.185 27.779 334.128
beta3_black[4] 39.640 73.269 0.132 32.310 188.962
beta3_black[5] 45238.850 1385340.635 0.086 32.769 10813.095
beta3_black[6] 5334.349 73380.905 0.071 32.379 12353.572
beta3_black[7] 232691.444 10106351.692 0.086 31.318 7238.643
beta3_black[8] 266.856 701.980 0.088 34.456 3088.076
beta3_black[9] 251.330 564.223 0.100 33.509 2350.254
beta3_black[10] 56.841 106.290 0.057 26.427 361.548
beta3_black[11] 68.638 54.131 18.397 45.235 230.495
beta3_black[12] 29.773 5.078 17.954 32.838 33.860
beta3_black[13] 39.279 0.674 37.711 39.349 40.374
beta3_black[14] 38.241 3.484 30.023 38.661 44.449
beta3_black[15] 44.567 40.484 8.994 38.492 130.077
beta3_black[16] 40.538 21.937 9.943 35.893 105.368
beta4_black[1] -0.284 0.190 -0.663 -0.279 0.084
beta4_black[2] 0.245 0.179 -0.105 0.240 0.622
beta4_black[3] -0.942 0.189 -1.314 -0.943 -0.576
beta4_black[4] 0.499 0.237 0.042 0.492 0.969
beta4_black[5] 0.259 2.808 -4.531 0.166 5.777
beta4_black[6] 0.290 2.667 -4.590 0.210 5.687
beta4_black[7] 0.320 2.822 -4.904 0.158 5.839
beta4_black[8] -0.727 0.367 -1.450 -0.727 -0.010
beta4_black[9] 1.532 1.020 -0.105 1.416 3.823
beta4_black[10] 0.020 0.186 -0.339 0.020 0.386
beta4_black[11] -0.701 0.210 -1.112 -0.698 -0.287
beta4_black[12] 0.322 0.344 -0.324 0.312 1.009
beta4_black[13] -1.209 0.221 -1.666 -1.203 -0.793
beta4_black[14] -0.107 0.234 -0.571 -0.111 0.363
beta4_black[15] -0.891 0.210 -1.297 -0.898 -0.476
beta4_black[16] -0.584 0.230 -1.027 -0.584 -0.126
mu_beta0_black[1] 1.224 0.705 -0.257 1.269 2.509
mu_beta0_black[2] 1.639 0.698 0.127 1.675 2.857
mu_beta0_black[3] 2.260 0.878 0.365 2.272 3.923
tau_beta0_black[1] 1.599 5.732 0.105 0.941 4.924
tau_beta0_black[2] 4.749 12.512 0.085 2.140 22.695
tau_beta0_black[3] 0.319 0.210 0.054 0.272 0.832
beta0_dsr[11] -2.834 0.294 -3.378 -2.835 -2.258
beta0_dsr[12] 0.243 3.200 -4.184 -1.154 4.899
beta0_dsr[13] -1.427 0.283 -1.970 -1.435 -0.873
beta0_dsr[14] -3.906 0.547 -4.991 -3.926 -2.834
beta0_dsr[15] -2.010 0.265 -2.568 -1.999 -1.492
beta0_dsr[16] -3.040 0.384 -3.793 -3.030 -2.303
beta1_dsr[11] 4.766 0.304 4.150 4.771 5.351
beta1_dsr[12] 6.526 2.147 2.917 6.595 10.667
beta1_dsr[13] 2.874 0.275 2.339 2.878 3.399
beta1_dsr[14] 6.551 0.564 5.420 6.566 7.665
beta1_dsr[15] 3.338 0.274 2.804 3.333 3.895
beta1_dsr[16] 5.832 0.395 5.085 5.824 6.619
beta2_dsr[11] -8.001 2.977 -15.944 -7.282 -4.840
beta2_dsr[12] -7.050 3.127 -14.554 -6.594 -1.868
beta2_dsr[13] -6.595 2.635 -12.844 -6.106 -2.089
beta2_dsr[14] -6.314 2.618 -11.183 -5.997 -2.556
beta2_dsr[15] -7.862 2.542 -13.921 -7.528 -4.112
beta2_dsr[16] -7.921 2.074 -11.858 -7.813 -4.483
beta3_dsr[11] 43.480 0.147 43.214 43.478 43.768
beta3_dsr[12] 46.583 9.951 33.197 48.929 66.068
beta3_dsr[13] 43.301 0.263 42.905 43.241 43.867
beta3_dsr[14] 43.328 0.191 43.085 43.276 43.805
beta3_dsr[15] 43.521 0.186 43.177 43.521 43.856
beta3_dsr[16] 43.441 0.159 43.179 43.426 43.765
beta4_dsr[11] 0.581 0.216 0.156 0.581 1.007
beta4_dsr[12] 0.246 0.445 -0.654 0.256 1.103
beta4_dsr[13] -0.115 0.217 -0.540 -0.108 0.293
beta4_dsr[14] 0.165 0.253 -0.329 0.165 0.658
beta4_dsr[15] 0.781 0.215 0.378 0.774 1.243
beta4_dsr[16] 0.172 0.226 -0.269 0.172 0.602
beta0_slope[11] -1.960 0.159 -2.265 -1.961 -1.645
beta0_slope[12] -4.620 0.213 -4.970 -4.637 -4.169
beta0_slope[13] -1.473 0.224 -2.096 -1.449 -1.109
beta0_slope[14] -2.654 0.181 -3.019 -2.650 -2.303
beta0_slope[15] -1.454 0.180 -1.812 -1.461 -1.089
beta0_slope[16] -2.763 0.173 -3.114 -2.763 -2.422
beta1_slope[11] 4.607 0.289 4.031 4.604 5.164
beta1_slope[12] 4.956 0.519 3.949 4.957 6.001
beta1_slope[13] 3.007 0.524 2.295 2.907 4.631
beta1_slope[14] 6.554 0.558 5.468 6.549 7.675
beta1_slope[15] 3.114 0.283 2.561 3.111 3.656
beta1_slope[16] 5.390 0.398 4.624 5.385 6.186
beta2_slope[11] 6.941 3.432 3.992 5.774 17.772
beta2_slope[12] 5.678 2.817 2.110 4.938 13.101
beta2_slope[13] 3.625 2.051 0.321 3.834 8.392
beta2_slope[14] 5.163 1.783 2.720 4.623 9.307
beta2_slope[15] 5.313 2.395 3.055 4.570 12.162
beta2_slope[16] 6.723 3.079 3.465 5.832 14.800
beta3_slope[11] 43.419 0.109 43.224 43.410 43.662
beta3_slope[12] 43.383 0.137 43.112 43.382 43.659
beta3_slope[13] 43.416 0.167 43.108 43.401 43.847
beta3_slope[14] 43.375 0.118 43.161 43.372 43.615
beta3_slope[15] 43.420 0.128 43.185 43.411 43.701
beta3_slope[16] 43.415 0.120 43.210 43.404 43.686
beta4_slope[11] -0.561 0.212 -0.996 -0.557 -0.154
beta4_slope[12] -1.412 0.659 -2.894 -1.331 -0.346
beta4_slope[13] 0.123 0.213 -0.300 0.121 0.540
beta4_slope[14] -0.156 0.260 -0.665 -0.157 0.351
beta4_slope[15] -0.672 0.220 -1.112 -0.666 -0.265
beta4_slope[16] -0.165 0.230 -0.623 -0.169 0.276
sigma_H[1] 0.215 0.048 0.131 0.212 0.321
sigma_H[2] 0.175 0.028 0.125 0.173 0.234
sigma_H[3] 0.190 0.039 0.120 0.187 0.272
sigma_H[4] 0.350 0.079 0.214 0.346 0.516
sigma_H[5] 0.942 0.213 0.553 0.933 1.400
sigma_H[6] 0.361 0.185 0.035 0.356 0.765
sigma_H[7] 0.305 0.063 0.206 0.297 0.459
sigma_H[8] 0.327 0.124 0.083 0.343 0.558
sigma_H[9] 0.522 0.129 0.329 0.502 0.822
sigma_H[10] 0.206 0.041 0.137 0.203 0.299
sigma_H[11] 0.274 0.045 0.197 0.270 0.374
sigma_H[12] 0.429 0.168 0.206 0.396 0.778
sigma_H[13] 0.221 0.037 0.156 0.218 0.300
sigma_H[14] 0.502 0.090 0.345 0.496 0.693
sigma_H[15] 0.251 0.039 0.186 0.248 0.339
sigma_H[16] 0.228 0.044 0.158 0.223 0.329
lambda_H[1] 3.390 4.708 0.167 1.847 15.168
lambda_H[2] 8.779 7.996 0.852 6.507 30.305
lambda_H[3] 6.646 9.430 0.304 3.450 34.786
lambda_H[4] 0.007 0.004 0.001 0.006 0.018
lambda_H[5] 1.750 4.077 0.019 0.395 17.242
lambda_H[6] 5.257 13.738 0.005 0.086 48.050
lambda_H[7] 0.013 0.009 0.002 0.010 0.036
lambda_H[8] 6.130 8.174 0.079 3.058 29.396
lambda_H[9] 0.017 0.012 0.003 0.014 0.048
lambda_H[10] 0.374 0.651 0.041 0.238 1.424
lambda_H[11] 0.267 0.436 0.010 0.112 1.376
lambda_H[12] 5.062 6.427 0.202 2.941 23.369
lambda_H[13] 3.672 3.437 0.194 2.717 12.732
lambda_H[14] 3.464 4.063 0.231 2.183 13.902
lambda_H[15] 0.023 0.027 0.003 0.016 0.089
lambda_H[16] 0.728 0.875 0.047 0.435 3.291
mu_lambda_H[1] 4.450 1.907 1.334 4.258 8.499
mu_lambda_H[2] 3.395 1.953 0.392 3.205 7.677
mu_lambda_H[3] 3.610 1.888 0.808 3.328 7.915
sigma_lambda_H[1] 8.757 4.313 2.238 8.100 18.326
sigma_lambda_H[2] 7.474 4.714 0.620 6.814 18.189
sigma_lambda_H[3] 6.464 3.986 1.085 5.664 16.277
beta_H[1,1] 6.900 1.070 4.324 7.073 8.476
beta_H[2,1] 9.870 0.472 8.827 9.898 10.723
beta_H[3,1] 7.975 0.746 6.223 8.082 9.178
beta_H[4,1] 10.097 7.613 -5.343 10.181 24.775
beta_H[5,1] -0.031 2.771 -5.317 0.041 5.118
beta_H[6,1] 2.137 4.649 -8.359 3.291 8.352
beta_H[7,1] 0.368 6.023 -12.048 0.685 11.536
beta_H[8,1] 1.043 3.108 -3.047 1.122 3.559
beta_H[9,1] 13.468 5.430 2.921 13.345 24.981
beta_H[10,1] 7.155 1.582 3.793 7.217 10.149
beta_H[11,1] 4.765 3.680 -3.236 5.463 9.946
beta_H[12,1] 2.633 1.021 0.878 2.576 4.916
beta_H[13,1] 9.046 1.030 6.937 9.142 10.521
beta_H[14,1] 2.165 1.013 0.142 2.182 4.086
beta_H[15,1] -6.442 3.748 -13.167 -6.711 1.685
beta_H[16,1] 3.344 2.565 -0.838 3.014 9.345
beta_H[1,2] 7.932 0.236 7.453 7.938 8.367
beta_H[2,2] 10.029 0.129 9.774 10.031 10.280
beta_H[3,2] 8.961 0.189 8.589 8.963 9.329
beta_H[4,2] 3.429 1.436 0.751 3.385 6.447
beta_H[5,2] 1.912 0.996 -0.004 1.896 3.819
beta_H[6,2] 5.527 1.198 2.888 5.660 7.430
beta_H[7,2] 2.685 1.153 0.590 2.609 5.124
beta_H[8,2] 2.993 1.017 1.228 3.119 4.382
beta_H[9,2] 3.214 1.053 1.096 3.220 5.201
beta_H[10,2] 8.201 0.322 7.549 8.210 8.811
beta_H[11,2] 9.844 0.664 8.843 9.732 11.273
beta_H[12,2] 3.970 0.361 3.294 3.954 4.706
beta_H[13,2] 9.146 0.267 8.700 9.129 9.673
beta_H[14,2] 4.026 0.352 3.345 4.020 4.731
beta_H[15,2] 11.433 0.681 9.979 11.485 12.668
beta_H[16,2] 4.429 0.791 2.920 4.432 5.992
beta_H[1,3] 8.551 0.231 8.125 8.541 9.026
beta_H[2,3] 10.099 0.110 9.885 10.098 10.328
beta_H[3,3] 9.657 0.156 9.357 9.655 9.983
beta_H[4,3] -2.176 0.848 -3.823 -2.176 -0.468
beta_H[5,3] 4.118 0.674 2.637 4.157 5.337
beta_H[6,3] 8.795 1.319 6.666 8.899 11.184
beta_H[7,3] -2.823 0.717 -4.203 -2.828 -1.377
beta_H[8,3] 5.486 0.526 4.748 5.396 6.705
beta_H[9,3] -2.431 0.725 -3.913 -2.423 -1.079
beta_H[10,3] 8.729 0.257 8.221 8.724 9.224
beta_H[11,3] 8.504 0.298 7.869 8.534 9.017
beta_H[12,3] 5.296 0.317 4.537 5.339 5.801
beta_H[13,3] 8.849 0.175 8.493 8.856 9.173
beta_H[14,3] 5.764 0.268 5.163 5.787 6.233
beta_H[15,3] 10.332 0.314 9.729 10.326 10.978
beta_H[16,3] 6.264 0.543 5.086 6.312 7.172
beta_H[1,4] 8.354 0.175 7.972 8.364 8.656
beta_H[2,4] 10.169 0.106 9.947 10.175 10.359
beta_H[3,4] 10.151 0.158 9.795 10.164 10.424
beta_H[4,4] 11.956 0.470 11.016 11.949 12.869
beta_H[5,4] 6.080 0.849 4.643 5.980 7.906
beta_H[6,4] 6.912 0.998 4.894 7.018 8.462
beta_H[7,4] 8.256 0.355 7.536 8.261 8.936
beta_H[8,4] 6.923 0.344 6.333 6.873 7.659
beta_H[9,4] 7.110 0.456 6.238 7.105 8.016
beta_H[10,4] 7.862 0.232 7.437 7.853 8.352
beta_H[11,4] 9.423 0.202 9.024 9.422 9.832
beta_H[12,4] 7.164 0.211 6.758 7.162 7.587
beta_H[13,4] 9.095 0.142 8.813 9.097 9.369
beta_H[14,4] 7.756 0.213 7.347 7.753 8.179
beta_H[15,4] 9.496 0.233 9.037 9.505 9.957
beta_H[16,4] 9.366 0.228 8.949 9.359 9.833
beta_H[1,5] 9.003 0.148 8.696 9.009 9.280
beta_H[2,5] 10.776 0.089 10.590 10.776 10.954
beta_H[3,5] 10.914 0.160 10.633 10.904 11.244
beta_H[4,5] 8.442 0.409 7.638 8.437 9.270
beta_H[5,5] 5.217 0.712 3.565 5.319 6.366
beta_H[6,5] 9.076 0.697 8.020 8.978 10.553
beta_H[7,5] 6.755 0.344 6.096 6.753 7.445
beta_H[8,5] 8.257 0.191 7.904 8.253 8.640
beta_H[9,5] 8.221 0.459 7.272 8.227 9.105
beta_H[10,5] 10.006 0.222 9.562 10.010 10.439
beta_H[11,5] 11.484 0.228 11.025 11.483 11.922
beta_H[12,5] 8.497 0.195 8.122 8.488 8.907
beta_H[13,5] 10.029 0.132 9.779 10.025 10.287
beta_H[14,5] 9.191 0.226 8.796 9.181 9.658
beta_H[15,5] 11.165 0.244 10.693 11.168 11.622
beta_H[16,5] 9.912 0.179 9.560 9.916 10.248
beta_H[1,6] 10.161 0.189 9.835 10.144 10.597
beta_H[2,6] 11.509 0.106 11.303 11.507 11.720
beta_H[3,6] 10.814 0.153 10.493 10.824 11.096
beta_H[4,6] 12.800 0.708 11.398 12.808 14.229
beta_H[5,6] 5.902 0.669 4.689 5.862 7.337
beta_H[6,6] 8.579 0.758 6.650 8.727 9.720
beta_H[7,6] 9.872 0.567 8.759 9.891 10.993
beta_H[8,6] 9.475 0.254 8.984 9.486 9.917
beta_H[9,6] 8.432 0.777 6.998 8.394 10.079
beta_H[10,6] 9.561 0.287 8.954 9.590 10.069
beta_H[11,6] 10.836 0.347 10.094 10.847 11.464
beta_H[12,6] 9.385 0.249 8.925 9.376 9.913
beta_H[13,6] 11.051 0.177 10.767 11.038 11.434
beta_H[14,6] 9.821 0.287 9.242 9.828 10.383
beta_H[15,6] 10.831 0.437 9.975 10.828 11.689
beta_H[16,6] 10.562 0.233 10.071 10.569 11.009
beta_H[1,7] 10.841 0.838 8.709 10.944 12.214
beta_H[2,7] 12.194 0.418 11.346 12.204 13.012
beta_H[3,7] 10.570 0.626 9.169 10.638 11.633
beta_H[4,7] 2.687 3.543 -4.442 2.563 9.763
beta_H[5,7] 6.599 2.440 2.328 6.356 12.464
beta_H[6,7] 9.793 2.978 4.611 9.465 17.416
beta_H[7,7] 10.464 2.874 4.808 10.477 16.113
beta_H[8,7] 10.974 0.966 9.388 10.885 13.086
beta_H[9,7] 4.518 4.018 -3.574 4.549 12.111
beta_H[10,7] 9.666 1.351 7.176 9.592 12.587
beta_H[11,7] 11.088 1.712 7.915 10.950 14.751
beta_H[12,7] 10.016 0.898 7.856 10.082 11.596
beta_H[13,7] 11.618 0.852 9.580 11.761 12.778
beta_H[14,7] 10.387 0.930 8.366 10.434 12.011
beta_H[15,7] 12.079 2.260 7.685 12.109 16.542
beta_H[16,7] 12.244 1.212 10.171 12.100 15.039
beta0_H[1] 8.804 13.487 -17.565 8.852 35.740
beta0_H[2] 10.557 5.977 -2.011 10.560 22.522
beta0_H[3] 9.817 9.286 -10.277 9.996 28.965
beta0_H[4] 11.271 177.440 -343.893 7.595 367.428
beta0_H[5] 4.045 36.142 -68.794 4.007 76.513
beta0_H[6] 6.416 63.926 -126.762 7.316 143.593
beta0_H[7] 2.756 135.231 -271.842 1.453 283.133
beta0_H[8] 5.915 27.589 -23.524 6.405 34.759
beta0_H[9] 6.138 112.907 -230.351 6.448 234.743
beta0_H[10] 8.440 29.787 -50.867 8.918 69.335
beta0_H[11] 10.258 51.362 -98.654 10.727 117.606
beta0_H[12] 6.843 11.385 -15.859 6.817 29.214
beta0_H[13] 9.680 14.341 -11.647 9.865 31.501
beta0_H[14] 7.328 11.009 -14.998 7.306 29.427
beta0_H[15] 9.268 111.806 -226.830 11.451 234.714
beta0_H[16] 7.641 25.526 -44.611 7.942 57.701